Changing locale of an existing database

Hi

I am using PostgreSQL 17 and would like to take advantage of performance
and stability across OS updates of builtin C.UTF-8 locale.
I have a cluster with a DB created with en_US.UTF-8 libc locale. I would
like to migrate the DB to C.UTF-8. Ideally there'd be an "ALTER DATABASE
... SET LOCALE ..." command that would take care of it but it seems it
doesn't exist. I was thinking that I could change the collation of all
TEXT/CHAR/VARCHAR columns in all the tables to pg_c_utf8, REINDEX all those
columns and change the default locale in the pg_database table.

Is it a sensible plan? Am I missing some steps? I can't find any reference
to anybody doing that before or discouraging it.

Thanks,
Marcin

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Marcin Gozdalik